Gravity gradiometer with flexural pivot bearing

ABSTRACT

A gravity gradiometer for measuring off-diagonal components of the gravitational gradient tensor includes a housing having a pair of electromagnetic shield enclosures (22, 23) arranged one inside the other, and a body (25) including superconducting material mounted within the inner enclosure (23) for fine pivotal flexure about an axis passing substantially through the centre of mass of the aforesaid body. An array of superconducting coils (30) is supported by the outer enclosure (22) and positioned in close proximity to the aforesaid body (25) for diamagnetically applying a rotational force to the body with respect to the axis of flexure and/or for responding by modulation of inductance to pivotal flexure of the body arising from a gravitational gradient across the body. The array is arranged to apply the rotational force in both rotational directions and to respond to flexure in either rotational direction. Also disclosed is a flexural pivot bearing which includes a pair of members (28, 31) with opposed close-spaced faces. These faces are joined by a web (29), of microscopic thickness, in a plane intersecting the faces. The members and the web are formed of an integral body of substantially uniform material, and the members are adapted for pivoted mutual flexure about a pivot axis aligned along said web.

This is a Continuation of application Ser. No. 08/115,677 filed Sep. 2, 1993, which is a continuaiton of application Ser. No. 07/688,528, filed as PCT/AU89/00543 Dec. 20, 1989, and both now abandoned.

FIELD OF THE INVENTION

This invention relates to a gravity gradiometer, especially a gradiometer for measuring off-diagonal components of the gravitational gradient tensor, and also provides a novel flexural pivot bearing which has particular, though certainly not exclusive, application to gravity gradiometry.

The gravimeter is widely employed in geological surveying to measure the first derivatives of the earth's gravitational potential function--the gravity field. Because of the difficulty in distinguishing spatial variations of gravity from temporal fluctuations of the accelerations of a moving vehicle, these measurements can be made to sufficient precision for useful exploration only with land-based stationary instruments. This difficulty is in principle avoided by measurement of the second derivatives of the potential--gravity gradients--but only limited success has been met to date in developing a satisfactory gradiometer instrument. Gravity gradiometry is thought especially appropriate to the location of geological structures bearing hydrocarbons, to geological mapping, and to locating high density (e.g., sulphides and iron ore) and low density (e.g., potash) mineral deposits.

Although it is not strictly correct to talk about the gradient of gravity, usage of the term has been universally adopted and will be used herein also. More formally, the second derivatives of the gravitational potential are termed gradients of gravity and constitute the gravity gradient tensor with components g_(xx), g_(xy) . . . g_(zz), adopting the convention of taking the Z-axis parallel to the local vertical. There are nine such components, only five of which are independent since the tensor is apparently symmetric and the potential is a scalar field obeying Laplace's equation.

BACKGROUND ART

The key elements of a gravity gradiometer are a pair of substantially identical spaced masses and the object is to measure differences between the gravitational force on the respective masses. Effectiveness requires measurements of this difference when it approaches only one part in 10¹² of normal gravity. Approaches to measuring gravity gradients have thus far fallen into two broad classes. The first of these entails differential modulation of a signal or parameter by the difference between the gravitationally induced accelerations of the two masses. The second technique involves direct measurement of the net gravitational acceleration of one mass relative to the other.

British patent publication 2022243 by Standard Oil Company discloses a gravity gradiometer in the first class. An element, described in the patent publication as a mass dipole dipoles as described, is mounted coaxially on one end of a photoelastic modulator element positioned in the cavity of a ring laser tube to differentially modulate circular polarization modes in response to application of a torque. In a preferred form, two mass dipoles as described are mounted on opposite ends of the modulator element to balance rotational acceleration noise. A closely related development by the same inventor, Lautzenhiser, described in U.S. Pat. No. 4,255,969, employs actual mass dipoles in conjunction with respective photoelastic modulator elements.

Another modulation technique involves rotating a platform which is supporting suitable arrangements of mass pairs. Various instruments of this kind are summarised by Jekeli at 69 EOS (No. 8). One of these, by Metzget, has been further developed and consists of electronically matched pairs of accelerometers on a rotating platform. The platform modulates the sum of opposing acceleration signals with a frequency twice its rotational frequency. These modulation systems call for extremely exacting uniformity in the rotation and require the use of bearing, rotational drive and monitoring technology which is not yet of a standard to render the instruments practicably suitable on an appropriate scale for airborne or moving land-based measurements for geophysical resource exploration, as opposed to geodetic surveying. The alternative of directly measuring gravity gradient components necessitates a weary high degree of electronic, magnetic, thermal and vibration isolation to achieve the measurement accuracy needed. Machines thus far have had poor spatial resolution and a high noise level.

An instrument for measuring the diagonal components g_(xx), g_(yy) and g_(zz) of the gravitational gradient tensor is described by van Kann et al in the publication IEEE Trans. Magn. MAG--21, 610 (1985) and further elaborated in the NERDDP End-Of-Grant Report (1986) on project no. 738. This instrument consists of a pair of accelerometers mounted with their sensitive axes in line. The difference in displacement of the accelerometers is proportional to the component of the given tensor gradient and is sensed by the modulated inductance of a proximate superconducting coil. This instrument suffers from the disadvantage that diaphragm springs serve both as mounts for the masses and as gradient sensors. The former of these roles calls for a greater stiffness in the springs while the sensing role necessitates enhancement of the springs' softness. It is also very difficult with the van Kann instrument to achieve axial alignment of the masses and trimming of the spring mountings with the accuracy needed to obtain the common mode acceleration rejection ratios necessary for the accuracy sought.

SUMMARY OF THE INVENTION

It has been realised, in accordance with a first aspect of the invention, that significant advantages can be obtained relative to the van Kann instrument, and direct measurement of gravitational gradients made more easily achievable, by instead measuring off-diagonal components of the gravitational gradient tensor by means of one and preferably two pivoted bodies supported by a flexural pivot, and by making the provision of mass support by the relatively stiff tensile spring property distinct from the sensing function provided by the relatively soft bending spring property.

The invention accordingly provides, in its first aspect, a gravity gradiometer for measuring off-diagonal components of the gravitational gradient tensor, which includes a housing comprising a pair of electromagnetic shield enclosures arranged one inside the other, and a body including superconducting material mounted within the inner enclosure for fine pivotal flexure about an axis passing substantially through the centre of mass of the aforesaid body. An array of superconducting coils is supported by the outer enclosure and positioned in close proximity to the aforesaid body for diamagnetically applying a rotational force to the body with respect to the axis of flexure and/or for responding by modulation of inductance to pivotal flexure of the body arising from a gravitational gradient across the body. The array is arranged to apply the rotational force in both rotational directions and to respond to flexure in either rotational direction.

The two enclosures are conveniently close fitting oblong boxes and the pivotally mounted body is preferably a matching solid body of a complementary shape. In a preferred embodiment, there is a superconducting coil on opposite sides of each arm of the body to either side of the flexure pivot axis. There may also be further coils to either side of the body at the axis and at each end of the body, for monitoring translational movement of the body.

The term "superconducting" is used herein, according to the normal convention, to denote a material which at least is superconducting below a characteristic critical temperature. A suitable such material is niobium, which has a critical temperature of about 9K.

The aforedescribed gravity gradiometer is of course preferably supported in a system which is shielded electrically, magnetically, thermally and vibrationally in a manner similar to that described in the aforementioned End-Of-Grant Report.

There are preferably a pair of gradiometers coupled together in a single instrument with the axes of flexure of their respective bodies parallel and preferably coincident, but with the bodies aligned mutually orthogonally and orthogonal to the axes of flexure.

The pivotal flexural mounting for the mass body may comprise a flexure bearing such as the commercially available Bendix pivot. It has been found, however, that this bearing is less than wholly satisfactory as it is constructed of several different metals secured together and this creates significant problems due to different thermal expansion coefficients and other parameter variations which become critical at the kind of accuracy desired in the present context.

The invention therefore provides, in a second aspect, a flexural pivot bearing which comprises a pair of members with opposed close-spaced faces. These faces are joined by a web, of microscopic thickness, in a plane intersecting the faces. The members and the web are comprised of an integral body of substantially uniform material, and the members are adapted for pivoted mutual flexure about a pivot axis aligned along said web.

A particularly useful application of the invention in its second aspect is as the mounting for the mass quadrupole body of the aforedescribed gravity gradiometer according to the first aspect of the invention. For this purpose the bearing is preferably cut from a single mass of a superconducting material such as niobium.

The two members of the bearing may be a generally annular body and a second body within the annular body.

In a more general third aspect, the invention provides a gravity gradiometer having broad application and not requiring vigorous sensitivity needing superconducting componentry comprising:

a housing;

a body mounted within the housing for fine pivotal flexure about an axis passing substantially through the centre of mass of said body; and

an array of transducer devices supported within said housing and positioned in close proximity to said body for applying a rotational force to said body with respect to said axis of flexure and/or for responding by modulation of inductance or capacitance to pivotal flexure of the body arising from a gravitational gradient across said body, wherein the array is arranged to apply said force in both rotational directions and to respond to flexure in either rotational direction. Preferably, in this case, said body is mounted by means of a flexural pivot bearing comprising a pair of members with opposed close-spaced faces, which faces are joined by a web, of microscopic thickness, in a plane intersecting the faces, wherein said members and said web are comprised of an integral body of substantially uniform material, and said axis of flexure is aligned along said web.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be described in greater detail, by way of example only, with reference to the accompanying drawings in which:

FIG. 1 is a diagrammatic axial cross-section of a gravity gradiometer assembly according to the first aspect of the invention supported on a gimballed mounting within a vacuum can for rotationally stabilised cryogenic operation;

FIG. 2 is an enlargement of part of FIG. 1, showing the gradiometer assembly at actual size;

FIG. 3 is a cross-section on the line 3--3 in FIG. 2;

FIG. 4 is an enlargement (5X magnification) of the flexural pivot bearing by which each of the mutually orthogonal mass quadrupole bars is supported in the gradiometer assembly;

FIG. 5A is a still greater enlargement (50X magnification) of the bearing in the region of the web;

FIG. 5B is a view similar to FIG. 5A of an alternative pivot bearing;

FIG. 6 is a more detailed axial cross-section of one of the coil/coil holder assemblies;

FIG. 7 and 8 are respective end elevations of the assembly shown in FIG. 6; and

FIGS. 9A-9C are a schematics of the superconducting circuit for the gradiometer.

BEST MODE OF CARRYING OUT THE INVENTION

The illustrated apparatus 10 includes a gradiometer assembly 12 supported by a biaxial or triaxial gimballed suspension 14 within a vacuum can 16. Apparatus 10 forms a dewar probe which may be suspended inside a dewar (not shown) and immersed therein in liquid helium. The can 16 provides an evacuable enclosure which can thereby be maintained at or near liquid helium temperature for cryogenic operation of gradiometer assembly 12. A thermal shield 17 may be fitted about the gradiometer assembly to reduce radiative and gas conductive heat transfer between the gradiometer assembly and the vacuum can. The entire equipment including the dewar is readily capable of being mounted in an aircraft or other moving vehicle.

Gradiometer assembly 12 in fact includes two substantially identical gradiometers, 20, 20' oriented to measure g_(xy) and g_(yx) components of the gravitational gradient tensor. The gradiometers 20, 20' are bolted above and below a central box structure 40 and each includes a pair of rectangular box enclosures 22, 23 e.g. of niobium, arranged one inside the other and outer niobium side plates 60 forming a surrounding shield from electromagnetic radiation. Enclosures 22, 23 are typically niobium and provide two further levels of all-round electromagnetic shielding.

A solid bar 25 of superconducting material such as niobium is mounted on a bearing 21 within the inner enclosure 23 for fine pivotal flexure about an axis 8 passing substantially through the centre of mass of the bar. The axes of flexure of the two bars 25, 25' are coincident and the bars extend in horizontal planes, mutually orthogonally in the x and y directions. The provision of a pair of orthogonal bars permits net elimination of common mode rotational accelerations i.e., rotational noise at each bar. The gradiometers can, of course, be oriented differently depending on the gradient components of interest.

Each gradiometer 20, 20' further includes an array of superconducting coils 30 which are mounted on holders 70 in turn supported by the outer enclosure 22. Coils 30 are positioned in close proximity to bar 25.

The dewar (not shown) would typically consist of an outer vacuum container, about 450 mm in diameter and 1.3 m high, and a 300 mm diameter inner well suspended from the mouth in the top of the outer shell by a fibreglass neck tube. The space between the inner well and the outer shell is permanently evacuated and typically fitted with thermal radiation shields surrounded by numerous layers of aluminised mylar superinsulation. Vacuum can 16 is supported within the dewar from an aluminium top plate which is attached to the mouth of the dewar. The top plate and vacuum can are joined by a neck tube 13 through which the vacuum can is evacuated, for example, down to the range of 10⁻⁸ to 10⁻⁰ Torr. Gimballed suspension 14 is attached to a rigid 25 mm thick aluminium plate 15 which is bolted to the bottom flange 15a of the neck tube and also forms a lid for can 16.

Gimballed suspension 14 consists of three gimbal frames 43, 44, 45 mounted on flexural pivots (not detailed) such as Bendix crossed-web pivots. Suspension 14 provides a triaxial rotational isolation for gradiometer assembly 12 and further incorporates respective fibre optic rotation sensors (not shown) for the x and y axes and associated superconducting electro-mechanical diamagnetic actuators for active stabilisation in a servo circuit controlled by the rotation sensors.

Instead of fibre optic rotation sensors, an optical remote sensing arrangement may be employed, permitting the stabilisation to be physically separated and enable the utilisation of a room temperature gyroscope. In this arrangement (not shown), a collimated beam of light from a laser or luminescent diode attached rigidly to a room temperature gyroscopic inertial reference system is reflected by a plane mirror attached rigidly to the gradiometer assembly. Rotation of the gradiometer assembly about any axis orthogonal to the light beam can then be sensed by measurement of the angle between the incident and reflected beams. This is accomplished by means of a position sensitive photo-detector mounted rigidly to the light source with its planar sensing surface normal to the beam. The detector actually measures the x and y coordinates of the position of the spot of light from the reflected beam and this is used to monitor the relative orientation of the gradiometer assembly. Isolation against mechanical vibration, is not illustrated but may be provided in established ways.

Vibrations travelling along the external instrumentation leads to the dewar maybe intercepted by the attachment of all cables near their mid-point to a massive lead block, itself suspended on a soft spring.

Each gradiometer 20, 20' is substantially identical and it is therefore now proposed to detail only the construction of gradiometer 20, with particular reference to FIGS. 2 and 3. As already mentioned, enclosures 22, 23 are of rectangular box-like configuration each made up of an assembly of top, bottom, side and end plates. Inner enclosure 23 is a close fit within outer enclosure 22 but arranged to be slid in and out on removal of the bottom plate of outer enclosure 22. The inner enclosure is provided with multiple circular openings 24 which respectively receive coil holders 70, and on its bottom plate 23a, with a bush 26 for the flexure bearing 21 that supports bar 25.

Flexure bearing 21 is detailed in enlarged FIGS. 4 and 5A, 5B and is formed by electric discharge machining (EDM) an almost continuous cut 27 through bar 25 parallel to axis 8, save for a microscopically thin web 29 extending the width of the bar along axis 8 at the centre of mass of the bar. In the example of FIG. 5A cut 27 defines a 270° part-cylindrical core 28 provided with three tapped holes 28a at one end for attachment of the core to bush 26. The core may of course be supported at both ends, if desired or necessary.

Further tapped holes (not shown) are provided in the bar to contain small screws whose position can be moved to partly achieve mass balance of the bar about axis 8. The radial portions 27a of cut 27 are deviated at their inner ends into right angle segments 27b which are aligned and separated by web 29. To either side of the web, the cut is bulged slightly at either side at 27c to lengthen the web and reduce its stiffness when acting as a pivot. Web 29 defines a micro-pivot some 0.030 mm thick, 0.200 mm long and 30 mm "wide", the width of bar 25. FIG. 5B shows an alternative cut to FIG. 5A.

It will be appreciated in particular from FIGS. 4 and 5A, 5B that core 28 and the adjacent inwardly projecting land 31 define a pair of members with opposed close-spaced regions 28b, 31b or 28b, 31b joined by web 29 in a plane extending the width of the bar. These members are adapted for pivotal mutual flexure about a pivot axis aligned along web 29. It will also be noted that members 28, 31 and the web are comprised of an integral body of substantially uniform material, in this case niobium. More particularly, the quadrupole bar 25 is capable of fine pivotal flexure on micro-pivot web 29 between angular limits determined by contact between the opposed faces of the radial portions 27a of cut 27. This angular limit is about 3 degrees and in any event is about the amount which would give rise to inelastic deformation of the web.

The dimensions of bar 25 are selected as 30.00 mm square by 90.0 mm long, thereby producing a gradient sensor with a natural frequency of about 1 Mz in which the sensitivity to accelerations via elastic deformations of the bar and pivot web 29 are made relatively small.

The mounting of each superconducting coil 30 is best seen in FIGS. 6 to 8. Each holder 70, a machined piece of niobium, is of circular cross-section and has an outer peripheral retaining flange 72. The holder further has a co-axial inner recess 71 for a fibreglass coil former 74. The coil 30 is a pancake coil, i.e., a flat spiral wound on the exposed surface of former 74 and held in place by epoxy. The wire 80, necessarily superconducting and conveniently niobium with formvar insulation, enters the centre of the spiral via a diagonal entrance hole 76 in former 74, circulates the former several times and exits through a channel in the former. Holes 75 in former 74 are for temporarily clamping the assembly during winding. Both wire ends pass through a hole 78 in holder 70 and then along various channels (not shown) machined in the outer faces of enclosure 22 and through holes into enclosure 40.

Holders 70 are held in place in registered apertures 24 in the enclosures and are covered by one of the shield plates 60, secured in place on the outer enclosure 22 by screws 73 or the like. Plates 60, of which there are four on the sides of each enclosure 22, shield the wires 80 which run from coils 30 to enclosure 40. The inner end of each coil is substantially co-planar with the inner face of the inner enclosure 23, in close proximity to a face of the bar 25.

The coils 30 are disposed with their axes in a common horizontal plane, three along each side and one at each end of the quadrupole bar. The side coils are arranged in opposed coaxial pairs, one pair with its axis co-planar with axis 8 and the others towards each end of bar 25. The end coils 30a, 30b on one side are utilised as push coils for diamagnetically applying a rotational force to, and augmenting the torsional stiffness of, the superconducting bar in the respective rotational directions about axis 8. The two opposite coils 30c, 30d on the other side are utilised for responding by modulation of their inductance to pivotal flexure of bar 25 arising from a gravitational gradient across the bar, the respective coils responding to flexure in the respective rotational directions about axis 8. The remaining four coils are also employed as sense coils, but for detecting translational movement of the bar in the x and y directions. The coils are substantially identical and may therefore be interchangeably employed as either push coils or sense coils, or both.

The push coils are required to provide feedback damping and to fine-tune the torsional resonant frequencies of the bars to precisely match their response to common mode angular accelerations about the axis 8.

It will be appreciated that bars 25 strictly need not be formed in solid superconducting material such as niobium, so long as they include superconducting material for interaction with coils 30. For example, each bar may be an aluminium mass lined with or treated to contain niobium at those parts of its surface which face the operational coils.

The eight coils of each set are wired in superconducting circuits as schematically depicted in FIG. 9 and detailed remarks concerning these circuits are set out hereinafter.

The superconducting wires 80 from the coils are fed through machined channels in enclosure 22 to a superconducting joint interface 41 within enclosure 40. The various required transformers are also housed within enclosure 40.

Further leads from this interface traverse feedthroughs 46 to the exterior of the assembly. The push coils are operated by employing heat switches to enable the insertion of controlled persistent currents while the means to detect inductance changes in the sense coils comprises one or more cryogenic SQUIDs (Superconducting Quantum Interference Devices) to sense differential motion. The heat switches and SQUIDs are housed within vacuum can 16. The switches and current source are typically under computer control.

As the SQUID sensing system is very sensitive to extremely small changes in magnetic flux, all leads and components are shielded by closed superconducting shields, e.g., of fine niobium tubing. External fields are exponentially attenuated as they enter the enclosure provided by the shields: the geometry of the tubing is designed so that the earth's ambient magnetic field produces less than one flux quantum inside the shield.

The illustrated apparatus, operated cryogenically, is capable of measuring angular displacements of the order of 10⁻¹² radians. It will be understood that materials other than niobium may be employed in the construction of the illustrated assembly. It is preferred however that the materials chosen have similar coefficients of thermal expansion, and that at least wires, wire shields and bar surfaces are formed in superconducting material. The enclosures, for good temperature control are desirably made in a material which is a good conductor of heat to minimise temperature gradients across the gradiometer. The preferred material for the gradiometer body (bars, enclosures, shields) is niobium.

Description of Superconducting Circuits (FIG. 9)

The preferred circuitry for the gradiometer consists of five circuits of three different types. These are the MAIN READOUT (FIG. 9A), the ACCELERATION MONITOR CIRCUITS (FIG. 9B) and the PUSH CIRCUITS (FIG. 9C). There are two acceleration monitor circuits, for measuring accelerations in the x and y directions, and two push circuits, for the respective bars 25, 25'. Before describing the three circuit types some general notes are appropriate:

1. The apparatus can, in principle, be oriented to measure any of the off-diagonal components of the gravity gradient tensor. Throughout the drawings, the figures all show a gradiometer with the z axis parallel to the vertical. FIG. 3, which shows the x axis parallel to the long axis of the bar, is the cross section of the lower coil enclosure as shown in FIG. 2. That is, the x axis is parallel with the long axis of the bottom bar 25 and the y axis is parallel with that of the top bar 25'.

2. In the circuits, the pancake coils used for sensing a superconducting surface of a bar are labelled according to their usage. Thus, PUSH I and PUSH 2 are push coils, X and Y are acceleration sense coils and θ+ and θ- are rotation sense coils.

3. The circuits consist of several elements. The output of each circuit is from a SQUID whose input is coupled to the rest of its circuit by means of a shielded toroidal air-cored transformer. Hence there are five SQUIDS, one for each circuit.

4. The inductors are of two types: toroida1 or flat spiral (pancake). All the coils which face a bar surface are pancake coils. The remainder of the inductors are toroidal.

5. In the illustrated instrument, a "heat switch" consists of a heater in close thermal contact with a thin superconducting tube which contains a loop of superconducting wire in good thermal contact with the tube but electrically insulated from it. The tube provides electromagnetic shielding for the loop which is a part of the superconducting circuit. By activating the heater, a part of the loop may be heated to a temperature above its superconducting transition temperature. This non-superconducting part then becomes an electrical resistor which will dissipate any current passing through the loop and will allow the injection of a new current via the pump leads.

In general, the design of heat switch may be refined or replaced by some other method which allows the dissipation and injection of currents in the superconducting circuits.

Although in principle, a gravity gradiometer is intrinsically insensitive to linear accelerations, in practice these accelerations may have an effect because of limitations in the achievable common mode acceleration rejection ratio and because of second order effects induced by elastic deformations of the micropivot web 29 and quadrupole bar 25, 25'. Consequently, accelerometers are required for the measurement of accelerations so that the acceleration effects may be appropriately subtracted from the gradient signal and so that the accelerations may be recorded for any subsequent analysis of the data.

The motion of the quadrupole bar 25 or 25' as a result of the aforementioned elastic deformations may be used as an accelerometer, or separate accelerometers may be mounted on board the gradiometer package to perform this function. In any case, two accelerometers are used, each measuring the linear accelerations parallel to the long axis of a bar. These are labelled X and Y according to the directions of these axes. The two acceleration monitor circuits (a representative one of which is shown in FIG. 9B), also labelled X and Y, simply perform the function of providing acceleration data for recording.

The two push circuits (one for each bar) are identical and only one is therefore shown in FIG. 9C. The following description for one applies equally to the other.

The push circuit loop carries a persistent current which can be adjusted and stored. The resulting magnetic flux in the loop means that the push coils act as magnetic springs thereby increasing the mechanical torsional resonant frequency of the bar. This technique is used to match the torsional resonant frequencies of the two bars. The rejection of angular accelerations about the z axis depends on how well these frequencies are matched. Modulations of the current will result due to angular motion of the bar and these are sensed by coupling the push loop to a SQUID. This output can be used in feedback to servo control angular accelerations about the z axis.

The main readout circuit depicted in FIG. 9A performs the function of combining the angular information from each of the responders together with the x and y acceleration information to provide a temperature compensated output signal proportional to the gravity gradient. There are five loops, in each of which the magnetic flux can be independently set and then locked. These are: the θ loop for the top bar; the θ loop for the bottom bar; the X acceleration loop (bottom bar); the Y acceleration loop (top bar); and finally a temperature sensing loop, into which the SQUID input transformer is coupled. Flux in the X, Y loops is trimmed so that the SQUID output is independent of these two accelerations. Similarly the flux in each of the two θ loops is set to cancel the effects of rotational acceleration about the z-axis. The temperature loop flux is adjusted to make a first order cancellation of small temperature inhomogeneities in the gradiometer. 

We claim:
 1. A gravity gradiometer for measuring off-diagonal components of a gravitational gradient tensor, comprising:a housing including a pair of electromagnetic shield enclosures arranged one inside the other; a body including superconducting material mounted within the inner of said enclosures for fine pivotal flexure about an axis passing substantially through the centre of mass of said body and wherein said body is mounted by means of a flexural pivot bearing comprising a pair of members with opposed close-spaced faces, which faces are joined by a web of microscopic thickness, in a plane intersecting the faces, wherein said members and said web are comprised of an integral body of substantially uniform material, and said axis of flexure is aligned along said web; and an array of superconducting coils supported by the outer of said enclosures and positioned in close proximity to said body for diamagnetically applying a rotational force to said body with respect to said axis of flexure and/or for responding by modulation of inductance to pivotal flexure of the body arising from a gravitational gradient across said body, wherein the array is arranged to apply said force in either rotational direction about said axis and to respond to flexure in either rotational direction about said axis.
 2. A gravity gradiometer according to claim 1 wherein said two enclosures are conveniently close fitting oblong boxes and said body is an oblong solid body of a shape complementary to said enclosures.
 3. A gravity gradiometer according to claim 1 wherein said axis of flexure divides said body into respective arms of said body to either side of said axis, and wherein there is a superconducting coil on opposite sides of each arm.
 4. A gravity gradiometer according to claim 3 wherein there are further coils to either side of the body at said axis and at each end of the body, for monitoring translational movement of said body.
 5. A gravity gradiometer according to claim 1 wherein said superconducting material is niobium.
 6. A gravity gradiometer according to claim 1 supported in a system which is shielded electrically, magnetically, thermally and vibrationally.
 7. A gravity gradiometer according to claim 1, wherein said two members of the bearing are a generally annular body and a second body within the annular body.
 8. A gravity gradiometer according to claim 1, wherein said bearing is cut from a single mass of a superconducting material.
 9. A gravity gradiometer according to claim 1 wherein one of said members is integral with said body.
 10. An instrument comprising a pair of gradiometers according to claim 4 coupled together in a single instrument with the axes of flexure of the respective bodies parallel, but with the bodies aligned mutually orthogonally and orthogonal to the axes of flexure.
 11. An instrument according to claim 10 wherein the arrays of superconducting coils associated with the two bodies are coupled into five superconducting loops in which magnetic flux of each loop can be independently set and locked, which loops include a first loop including coil(s) at one or both ends of one of the bodies, a second loop including coil(s) at one or both ends of the other of the bodies, third and fourth loops including the coils to apply rotational force to and/or respond to pivotal flexure of the respective bodies, and a fifth loop responsive to the temperature about the bodies.
 12. An instrument according to claim 10, wherein the axes of flexure of said respective bodies are substantially co-incident.
 13. A gravity gradiometer comprising:a housing; a body mounted within the housing for fine pivotal flexure about an axis passing substantially through the centre of mass of said body; and an array of transducer devices supported within said housing and positioned in close proximity to said body for applying a rotational force to said body with respect to said axis of flexure and/or for responding by modulation of inductance or capacitance to pivotal flexure of the body arising from a gravitational gradient across said body, wherein the array is arranged to apply said force in either rotational direction about said axis and to respond to flexure in either rotational direction about said axis, wherein said body is mounted by means of a flexural pivot bearing comprising a pair of members with opposed close-spaced faces, which faces are joined by a web, of microscopic thickness, in a plane intersecting the faces, and wherein said members and said web are comprised of an integral body of substantially uniform material, and said axis of flexure is aligned along said web.
 14. A gravity gradiometer according to claim 13, wherein one of said members is integral with said body.
 15. A gravity gradiometer according to claim 13 wherein said two members of the bearing are a generally annular body and a second body within the annular body.
 16. An instrument comprising a pair of gradiometers according to claim 13 coupled together in a single instrument with the axes of flexure of their respective bodies parallel, but with the bodies aligned mutually orthogonally and orthogonal to the axes of flexure. 